Reasons why infinity hasn't been implemented into modern math

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Discussion Overview

The discussion centers around the role of infinity in modern mathematics, particularly why it is not treated as a numerical entity like zero. Participants explore various mathematical contexts where infinity is utilized, debate its classification, and express differing opinions on its treatment in educational settings.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants argue that infinity should be numerically defined in a way similar to zero, suggesting that it could be integrated into algebraic properties.
  • Others point out that infinity is already present in modern mathematics through concepts like extended real numbers, cardinal numbers, and projective geometry.
  • A few participants emphasize that infinity is treated differently in various mathematical contexts, such as limits and functions, and that its notation is not typically used in basic algebra.
  • There are claims that low-level algebra defines infinity as undefined, which some participants contest, arguing that it is more about the context of teaching than an actual definition.
  • Some express frustration over the vague use of the term "infinity" without specifying the type of infinity being referenced, suggesting that clarity in terminology could improve discussions.
  • Participants discuss the implications of defining operations with infinity and the potential confusion it may cause for learners.
  • There are mentions of the philosophical aspects of defining numbers and the role of zero in mathematics, with some arguing for the necessity of defining infinity similarly.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the treatment of infinity in mathematics. While some agree that infinity is implemented in various forms, others maintain that it is not adequately defined or utilized numerically in basic mathematics.

Contextual Notes

Limitations in the discussion include varying definitions of infinity, the context in which it is taught, and the different mathematical frameworks that utilize infinity, which may not be universally understood or accepted.

  • #61
What I meant to say, and I apologize if this was actually unclear, is that sometimes the currently accepted definition is not the final word in the definition. Perhaps a better, more useful definition is possible. I think I'm done with this thread.
 
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  • #62
To be fair, there are also uses (convergence of infinite products, for example) where 0 is not considered a finite number. But the usual definition of finite number, to me, is "between two integers" which of course includes 0.
 
  • #63
csprof2000 said:
What I meant to say, and I apologize if this was actually unclear, is that sometimes the currently accepted definition is not the final word in the definition.
Final word??
THIS is what you actually said:
How can you call 0 finite?

Have you ever given it any thought, or are you just parroting conventional wisdom?
This is very clear. Here, you are advocating the ideas that:
1. It is FALSE to call 0 a finite number
and
2. That the evil "establishment" somehow have brainwashed people into thinking that 0 might be a finite number.

There is nothing ambiguous in what you wrote, and your last post is just a shameful cop-out.
Perhaps a better, more useful definition is possible.
As in your previous empty blather?
I think I'm done with this thread.
how considerate of you.
 
  • #64
This is the most bipolar thread I've ever seen, intensely funny and depressing. Everyone knows more about math than the mathematicians. Especially CS people (no offense to those who actually take the time to understand the concepts they are abusing, if you exist). The last time I read a post by CSProf he was trying to convince me that the reals are countable!
 
  • #65
Hasn't people yet learned that mathematics is not science and we somehow have "arbitrary definitions"?

Do they know the definition of what definition is?

I think we defined things way they are because... because... damn I cannot remember. But I am sure there's a reason! And I am sure they will keep discovering reasons why it should be wrong! [/sarcasm]
 
  • #66
I suggest that we adopt the following rule:
\frac{\Infinity}{\Infintity}=1
 
  • #67
You mean as in

3237+ 2343= 1

213/234= 1

e3243= 1?

Certainly would simplify arithmetic!
 

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